Question

calculating and interpreting a z - score
tennis balls must have a height rebound, or bounce, that is approved by the international tennis federation as measured by dropping a ball from a height of 100 inches and measuring how high it bounces. approved balls must bounce back up 53 to 58 inches.
annie coach tested 50 tennis balls and found that the mean bounce was 56.2 inches and the standard deviation was 1.8 inches.
the z - score of a ball that bounces 56.2 inches is
this ball has a bounce that is the mean.

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Plug in given values

We know $x=56.2$, $\mu=56.2$, $\sigma=1.8$. Substitute into the formula:
$z = \frac{56.2 - 56.2}{1.8}$

Step3: Calculate the z-score

Simplify the numerator first: $56.2 - 56.2 = 0$. Then $\frac{0}{1.8} = 0$.

Step4: Interpret the z-score

A z-score of 0 means the data point is equal to the mean.

Answer:

The z-score of a ball that bounces 56.2 inches is $\boldsymbol{0}$.
This ball has a bounce that is $\boldsymbol{equal to}$ the mean.